Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problems (IVPs) compared to other approaches found in the literature, which is verified by the obtained solutions. The determination of the transient solutions for Markov chains is presented using the proposed method. The results show better accuracy in solving the transient distribution in Markov chains, which implies that there is an improved assurance in adopting this approach in future studies of the Markov chain modeling process for predicting future events based on the current state of a process. Future studies on Markov chain modeling could adopt the introduced method to predict future events based on the current state of a process.
Many athletes believe that it enhances the level of performance during training and competition, in addition to compensating for fluids during exercise when the levels of temperature and humidity in the atmosphere rise during the athlete's intensive training, as it increases the requirements for fluid compensation to avoid the risk of potential thermal disorders. If training continues for more than an hour causing fatigue, athletes are advised to drink carbohydrate drinks that quickly convert to glucose in the blood, while sodium should be included in the fluids consumed during exercise or matches that last more than (1-2 hours). The effect of drinking a drink containing 12% carbohydrates and electrolytes before each half of a simul
... Show MoreThe purpose of my thesis is to synthesis two new bidentate ligands which were used to prepare series of metal complexes by reacting the ligands with (M+2 = Mn, Co, Ni, Cu, Cd and Hg) Succinyl chloride was used as starting material to synthesis two bidentate ligands (L1) and (L2) by reaction it with 4-chloroaniline (L1) and (4-aminoacetophenone) (L2) in dichloromethane as a solvent, that are: (L1) = N1,N4-bis (4-chloro phenyl ) succinamide (L2) =N1,N4-bis(4-acetylphenyl)succinamide The new ligands were characterize by using spectroscopic study (Fourier-transform infrared spectroscopy (FT-IR), electronic spectra ( UV-Vis) ,nuclear magnetic resonance(1H,13C-NMR), Mass spectra
... Show MoreIn the present work, a study is carried out to remove chromium (III) from aqueous solution by: activated charcoal, attapulgite and date palm leaflet powder (pinnae). The effect of various parameters such as contact time, and temperature has been studied. The isotherm equilibrium data were well fitted by Freundlich and Langmuir isotherm models. The adsorption capacity of chromium (III) that was observed by activated charcoal, attapulgite and date palm leaflet powder (pinnae) increased with the rise of temperature when the concentrations of Cr (III) were 600, 700 and 100mg/L respectively. The greatest adsorption capacity ofactivated charcoal, attapulgite and date palm leaflet powder (pinnae) at 10°C was 7.51, 5.39 and 0.77mg.gˉ¹ respective
... Show MoreIn this study, Al2O3 thin films were prepared by dc reactive sputtering technique using different gas mixtures of argon and oxygen gases (90:10, 70:30, 50:50, 30:70, and 10:90). These films were characterized to introduce their surface morphology and elemental composition as functions of the oxygen content in the gas mixture. The gas mixing ratio plays a crucial role in controlling the nanoscale morphology of the prepared thin films. The [Al]/[O] ratio varies non-linearly with the Ar:O2 mixing ratio. Increasing the oxygen content leads to a progressive decrease in surface roughness, resulting in smoother and more uniform films with finer granular features. These results presented herein are useful to optimize the sputtering process to ac
... Show MoreA new ligand N-((4-(phenylamino) phenyl) carbamothioyl) acetamide (PCA) was synthesized by reaction of (4-amino di phenyl amine) with (acetyl isothiocyante) by using acetone as a solvent. The prepared ligand(PCA) has been characterization by elemental analysis (CHNS), infrared(FT-IR),electronic spectral (UV-Vis)&1H,13C- NMR spectra. Some Divalent Metal ion complexes of ligand (PCA) were prepared and spectroscopic studies by infrared(FT-IR), electronic spectral (UV-Vis), molar conductance, magnetic susceptibility and atomic absorption. The results measured showed the formula ofFall prepared complexes were [M (PCA)2 Cl2] (M+2 = Mn, Co, Ni, CU, Zn, Cd &Hg),the proposed geometrical structure for all complexes wereeoctahedral.
This study was done to evaluate a new technique to determine the presence of methamphetamine in the hair using nano bentonite-based adsorbent as the filler of extraction column. The state of the art of this study was based on the presence of silica in the nano bentonite that was assumed can interact with methamphetamine. The hair used was treated using methanol to extract the presence of methamphetamine, then it was continued by sonicating the hair sample. Qualitative analysis using Marquish reagent was performed to confirm the presence of methamphetamine in the isolate.The hair sample that has been taken in a different period confirmed that this current developing method can be used to analyzed methamphetamine. This m
... Show More